Kasim can so a piece of work in `7 1/2` hours and Sunil can finish it in 10 hours. If Kasim works at it for 3 hour and Sunil for 4 hours the amount of work left unfinished is-

Options

A. `1/5`
B. `2/5`
C. `1/4`
D. `2/7`

Answer

To solve the problem, we need to determine how much work is left unfinished after Kasim and Sunil have worked for a certain amount of time. Here’s a step-by-step solution:

### Step 1: Determine the total work in units.
Kasim can complete the work in \(7 \frac{1}{2}\) hours, which is equivalent to \(7.5\) hours. To express this in a more manageable form, we convert it to an improper fraction:
\[ 7 \frac{1}{2} = \frac{15}{2} \text{ hours} \]
Sunil can complete the work in \(10\) hours.

To find the total work in units, we can take the least common multiple (LCM) of the two times:
- The LCM of \(15\) and \(10\) is \(30\).

### Step 2: Calculate the work done by each person in one hour.
Next, we find out how much work each person can do in one hour:
- Kasim's work rate:
\[ \text{Work done by Kasim in 1 hour} = \frac{30 \text{ units}}{\frac{15}{2} \text{ hours}} = \frac{30 \times 2}{15} = 4 \text{ units/hour} \]
- Sunil's work rate:
\[ \text{Work done by Sunil in 1 hour} = \frac{30 \text{ units}}{10 \text{ hours}} = 3 \text{ units/hour} \]

### Step 3: Calculate the total work done by Kasim and Sunil.
Kasim works for \(3\) hours and Sunil works for \(4\) hours. We can calculate the total work done by each:
- Work done by Kasim:
\[ \text{Work done by Kasim} = 3 \text{ hours} \times 4 \text{ units/hour} = 12 \text{ units} \]
- Work done by Sunil:
\[ \text{Work done by Sunil} = 4 \text{ hours} \times 3 \text{ units/hour} = 12 \text{ units} \]

### Step 4: Calculate the total work done.
Now, we can find the total work done by both:
\[ \text{Total work done} = 12 \text{ units (Kasim)} + 12 \text{ units (Sunil)} = 24 \text{ units} \]

### Step 5: Determine the total work and the unfinished work.
The total work is \(30\) units (as calculated from the LCM). Therefore, the unfinished work is:
\[ \text{Work left} = \text{Total work} - \text{Total work done} = 30 \text{ units} - 24 \text{ units} = 6 \text{ units} \]

### Step 6: Express the unfinished work as a fraction of the total work.
To express the unfinished work as a fraction of the total work:
\[ \text{Fraction of work left} = \frac{6 \text{ units}}{30 \text{ units}} = \frac{1}{5} \]

Thus, the amount of work left unfinished is \(\frac{1}{5}\).